quasiIso_forget₂_εToSingle₀ — Mathlib

English

Another articulation of the forget₂-εToSingle₀ quasi-isomorphism.

Русский

Ещё одно оформление квазиизоморфизма forget₂-εToSingle₀.

LaTeX

$$QuasiIso forget₂_εToSingle₀$$

Lean4

theorem quasiIso_forget₂_εToSingle₀ :
    QuasiIso (((forget₂ _ (ModuleCat.{u} k)).mapHomologicalComplex _).map (εToSingle₀ k G)) :=
  by
  have h : QuasiIso (forget₂ToModuleCatHomotopyEquiv k G).hom := inferInstance
  rw [← εToSingle₀_comp_eq k G] at h
  exact quasiIso_of_comp_right (hφφ' := h)

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